Example 7.3.7.7. In the situation of Corollary 7.3.7.6, suppose that $\operatorname{\mathcal{B}}= \Delta ^0$. Corollary 7.3.7.6 then asserts that a morphism $e: X \rightarrow Y$ in the functor $\infty $-category $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ is $V'$-cocartesian if, for every object $C \in \operatorname{\mathcal{C}}$, the induced map $e_{C}: X(C) \rightarrow Y(C)$ is a $V$-cocartesian morphism of $\operatorname{\mathcal{D}}$. This is a special case of Lemma 5.2.1.5.
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